In Fig 10.23, triangle ABC is an isosceles triangle in which AB = AC. D,E and F are the midpoints of sides AB,BC and CA respectively. Prove that triangle DBE congruent triangle FCE.
Answers
Answer:
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Step-by-step explanation:
Given In AABC, AB = AC and D, E and P are the mid-points of the sides BC, AC and AB, respectively.
image
To prove DE=DF
Proof In AABC, we have
AB=AC
1/2 * A * B = 1/2 * A * C
BF=CE
ZC = ZB ... (ii)
[AB = AC and angles opposite to equal
sides are equal]
Now, in A BDF and A CDE, DB = DC
[ D is the mid-point of BC]
BF = CE [from Eq. (i)]
and C= 2B [from Eq. (ii)]
image
Hence, DF = DE
Given In AABC, AB = AC and D, E and P
are the mid-points of the sides BC, AC and AB, respectively.
image
To prove DE=DF
Proof In AABC, we have
AB=AC
1/2 * A* B = 1/2* A* C
BF=CE
ZC = ZB ... (ii)
[AB = AC and angles opposite to equal sides are equal]
Now, in A BDF and A CDE, DB = DC
[D is the mid-point of BC]
BF = CE [from Eq. (i)]
and C= 2B [from Eq. (ii)]
image
Hence, DF = DE
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